up to a polynomial factor depending only on the gradients as well. Second aspect has to do with the critical terms that emerge from the topological component of the \(e\) -equation in the form of quartic products. To achieve control on such terms under the criterion assumption (REF ) we employ paraproduct estimates that are inspired by the proof of the positive side of the Onsager conjecture for incompressible Euler equation [1]}, see [2]} for the full overview of this subject.
